The proposal is a part of recommendations Obama made recently to the supercommittee of lawmakers that is tasked with recommending $1.5 trillion or more in cuts from the federal deficit by Thanksgiving. The president is also recommending a $7.50 increase in the security taxes passengers pay each way on trips.

The airline industry has said the proposal would cost it $36 billion, and Calio said Tuesday that airlines would not be able to pass the costs on to customers in fare increases.

"Airline tickets are priced to sell," he said. "No airline wants or can afford empty seats in the sky. The basics of the industry are matching supply to demand, at prices customers will pay and that at least hopefully cover costs.

"Price elasticity, a concept most of our policymakers don't seem to understand, makes it extremely difficult for airlines to pass on additional costs to passengers," he continued. "This is probably one of the biggest misconceptions about the industry: that an airline can simply increase a fare by even a few dollars without impacting demand."

The ATA has launched a campaign in opposition to the proposal called "Stop Air Tax Now."

At least one airline, Southwest, has echoed the organization's message. In a blog post this week, Southwest CEO Gary Kelly called on the airline's customers to contact their lawmakers.

"The increase in taxes is a cost our airline, our passengers, and our industry simply cannot absorb without having devastating effects on our business and the overall U.S. economy," Kelly said.